Look at how they are formed in Russian:

• 22 is два́дцать две́ [feminine] or два́дцать два [masculine or neuter] (therefore, it uses the noun form for две/два),
• 23 is два́дцать три (therefore, it uses the noun form for три),
• 42 is два́дцать два/две,
• 53 is пятьдеся́т три,
• 64 is шестьдеся́т четы́ре.

At the same time, numbers from 11 to 19 are formed differently (the pattern was like 'one-on-ten', 'two-on-ten'):

• двена́дцать ends in -дцать, which is a contracted form of десять and therefore you use the noun form for десять,
• трина́дцать ends in -дцать,
• четы́рнадцать ends in -дцать.

The way these numbers are formed is really an exception (for ten, you use 'one-on-ten' pattern; for other tens, you use 'twenty one' pattern), but the noun form choice doesn't seem too illogical to me.